Question

In the quadrilateral ABCD, ∠A = ∠C = 110°, ∠B = 60°. DE = DF. The measure of angle x is ______.

विकल्प

• 120°

• 130°

• 100°

• 80°

Answer 1

In the quadrilateral ABCD, ∠A = ∠C = 110°, ∠B = 60°. DE = DF. The measure of angle x is 130°.

Explanation:

We are given:

• A quadrilateral ABCD with:
  • ∠A = ∠C = 110°
  • ∠B = 60°
• DE = DF   ...(Implying triangle ΔDEF is isosceles)
• Need to find angle x = ∠EFG

Step-by-step:

Step 1: Use angle sum in quadrilateral

∠A + ∠B + ∠C + ∠D = 360°

110° + 60° + 110° + ∠D = 360°

⇒ ∠D = 80°

Step 2: Triangle ΔDEF is isosceles

Since DE = DF, triangle ΔDEF has ∠E = ∠F

Also, from above, ∠EDF = ∠D = 80°

So, ∠E + ∠F = 180° – 80° = 100°

⇒ ∠E = ∠F = `100^circ/2` = 50°

Step 3: Find x = ∠EFG

Angle x is the linear pair to ∠F = 50°, 

So, x = 180° – 50° = 130°.